Annata,
Like Sarah said, great question!
Your mother does need to know Microsoft Word (or another word processing program), Internet Explorer (or Mozilla, Safari, etc.), Adobe Acrobat, and some sort of media player so she can view videos. Like Sarah mentioned, it depends on the course what things she will be using since buisness classes or classes involving statistics will use programs like Excel whereas courses on education can use things like "Inspiration" or "TeacherTube." Usually, in the syllabus, there is a list of the programs that are being used.
In both my undergraduate and graduate work I found that my professors also used an online website called "Blackboard." If you are unfamiliar with it, it's a website that you log into, then log into your class. Once on the site you will see a list of tabs on the side that include: assignments, discrussion boards, syllabus, professor information, videos, and a place to email.
I would say that if your mother can get on a computer to type something up, check her email, maneuver through a site, and watch a video than she is probably fine. However, I will stress that she should talk to the professor or college before she signs up for anything. Many schools are willing to help students with computers, but she doesn't want to have to get help in the middle of a course. Help should come first.
I hope that helped answer your question. Thanks for posting it!
-Elizabeth